Michael Duberry was sent off after hauling down Miller with five minutes left, but the Scot was denied by Leeds goalkeeper Sullivan from the spot.
Leeds will be happy with a point after Lucas Radebe was carried off after only 18 minutes, and they were forced to survive sustained Wolves pressure.
Sullivan was the hero, denying Miller from long range and saving well from Colin Cameron and Leon Clarke.
Leeds boss Kevin Blackwell:
"If you're coming to Molineux, the first priority is to secure a point and we did that.
"Credit has to go to our goalkeeping coach because he really did his homework.
"He'd been watching all the videos and had been working with 'Sulli' on penalties yesterday. When the ref awarded the penalty he just turned to us on the bench and said 'Sulli knows which way Miller's going'.
"I believe he's going to go on to become a very good signing."
Wolves: Jones, Clyde, Olofinjana, Craddock,
Naylor (Andrews 81), Newton, Ince, Cameron (Cooper 89), Edwards, Miller, Clarke. Subs Not Used: Oakes, Mulligan, Lowe.
Leeds: Sullivan, Kelly, Butler, Duberry, Crainey,
Richardson (Guppy 89), Radebe (Walton 18), Wright, Pugh, Ricketts (Joachim 68), Deane. Subs Not Used: Carson, Kilgallon.
Sending Off: Duberry (86).
Ref: G Laws (Tyne & Wear).